A207873 Numerator of Z(n,1/2), where Z(n,x) is the n-th Zeckendorf polynomial.

1, 1, 1, 5, 1, 9, 5, 1, 17, 9, 5, 21, 1, 33, 17, 9, 41, 5, 37, 21, 1, 65, 33, 17, 81, 9, 73, 41, 5, 69, 37, 21, 85, 1, 129, 65, 33, 161, 17, 145, 81, 9, 137, 73, 41, 169, 5, 133, 69, 37, 165, 21, 149, 85, 1, 257, 129, 65, 321, 33, 289, 161, 17, 273, 145, 81, 337

Offset

1,4

Comments

The Zeckendorf polynomials Z(x,n) are defined and ordered at A207813. See A207872 for denominators to match A207873.

Links

Table of n, a(n) for n=1..67.

Mathematica

fb[n_] := Block[{k = Ceiling[Log[GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[fr, 1]; t = t - Fibonacci[k],
    AppendTo[fr, 0]]; k--]; fr]; t = Table[fb[n],
      {n, 1, 500}];
b[n_] := Reverse[Table[x^k, {k, 0, n}]]
p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]
Table[p[n, x], {n, 1, 40}]
Denominator[Table[p[n, x] /. x -> 1/2,
   {n, 1, 120}]]                       (* A207872 *)
Numerator[Table[p[n, x] /. x -> 1/2,
   {n, 1, 120}]]                       (* A207873 *)

Crossrefs

Cf. A207813, A207873.

Sequence in context: A094650 A189234 A199736 * A198671 A129343 A342634

Adjacent sequences: A207870 A207871 A207872 * A207874 A207875 A207876

Keyword

nonn

Author

Clark Kimberling, Feb 21 2012

Status

approved